Originally Posted by Island Don

What he said!

I've owned a lot of MINIs, both Justa, S, and JCWs and would never dream of representing anything other than the factory JCW as a "JCW".

One other obvious differentiator when looking at a car is the brakes. To add the JCW brakes to an S is crazy expensive (parts list at over $2k), so I'd be surprised to see very many people do that mod even though MINI offers it.
Not that it's not worth doing (love the JCW brakes), but aftermarket big brake kits can be much less expensive, or better for the price.

If you add the tune, brakes, aero kit, wheels, interior etc. to an S, you would have been better off just buying the factory JCW to start with.